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Expression simplification/ Factor perfect squares/ y^2-7*y*x+5*x^2

Factor y^2-7*y*x+5*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  - 7*y*x + 5*x
$$5 x^{2} + \left(- x 7 y + y^{2}\right)$$ 
y^2 - 7*y*x + 5*x^2
General simplification [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    y*\7 - \/ 29 /| |    y*\7 + \/ 29 /|
|x - --------------|*|x - --------------|
\          10      / \          10      /
$$\left(x - \frac{y \left(7 - \sqrt{29}\right)}{10}\right) \left(x - \frac{y \left(\sqrt{29} + 7\right)}{10}\right)$$ 
(x - y*(7 - sqrt(29))/10)*(x - y*(7 + sqrt(29))/10)
The perfect square
Let's highlight the perfect square of the square three-member
$$5 x^{2} + \left(- x 7 y + y^{2}\right)$$
Let us write down the identical expression
$$5 x^{2} + \left(- x 7 y + y^{2}\right) = - \frac{29 y^{2}}{20} + \left(5 x^{2} - 7 x y + \frac{49 y^{2}}{20}\right)$$
or
$$5 x^{2} + \left(- x 7 y + y^{2}\right) = - \frac{29 y^{2}}{20} + \left(\sqrt{5} x - \frac{7 \sqrt{5} y}{10}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{29}{20}} y + \left(\sqrt{5} x + - \frac{7 \sqrt{5}}{10} y\right)\right) \left(\sqrt{\frac{29}{20}} y + \left(\sqrt{5} x + - \frac{7 \sqrt{5}}{10} y\right)\right)$$
$$\left(- \frac{\sqrt{145}}{10} y + \left(\sqrt{5} x + - \frac{7 \sqrt{5}}{10} y\right)\right) \left(\frac{\sqrt{145}}{10} y + \left(\sqrt{5} x + - \frac{7 \sqrt{5}}{10} y\right)\right)$$
$$\left(\sqrt{5} x + y \left(- \frac{7 \sqrt{5}}{10} - \frac{\sqrt{145}}{10}\right)\right) \left(\sqrt{5} x + y \left(- \frac{7 \sqrt{5}}{10} + \frac{\sqrt{145}}{10}\right)\right)$$
$$\left(\sqrt{5} x + y \left(- \frac{7 \sqrt{5}}{10} - \frac{\sqrt{145}}{10}\right)\right) \left(\sqrt{5} x + y \left(- \frac{7 \sqrt{5}}{10} + \frac{\sqrt{145}}{10}\right)\right)$$
Common denominator [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Powers [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Numerical answer [src] 
y^2 + 5.0*x^2 - 7.0*x*y
y^2 + 5.0*x^2 - 7.0*x*y
Rational denominator [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Trigonometric part [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Assemble expression [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Combinatorics [src] 
 2      2        
y  + 5*x  - 7*x*y
$$5 x^{2} - 7 x y + y^{2}$$ 
y^2 + 5*x^2 - 7*x*y
Combining rational expressions [src] 
   2              
5*x  + y*(y - 7*x)
$$5 x^{2} + y \left(- 7 x + y\right)$$ 
5*x^2 + y*(y - 7*x)
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